Snowmobiles and ATVs generally employ a continuously variable transmission (“CVT”) having opposing sheaves and a belt that drives a driven shaft as part of the power transmission. CVTs include a drive clutch and a driven clutch that receives power from the drive clutch. As with many other components of an engine, these components generate heat that can harm engine components. For example, heat is generated due to the friction between the belt and the clutch sheaves. The problem is especially acute with high engine speeds and relatively low vehicle speeds, such as when a mountain snowmobile is riding through deep powder snow or when a utility snowmobile is performing a chore with engine time at idle or slow vehicle speeds. A driven clutch may have cooling vanes that move air to cool the belt as the vanes move. However, the driven clutch does not move when the vehicle idles and moves slower than the drive clutch with a load on the system. Clutch belts can lose strength and optimum stiffness and can even rupture at high temperatures. Running a powered fan is not typically a viable solution for various reasons. Space in an engine compartment is limited, so most engine compartments simply do not have room for a bulky fan and motor. In addition, a motored fan will generate heat itself, which may lessen the overall effect of such a system. Perhaps most importantly, an electric fan would add excessive weight to snowmobiles that manufacturers painstakingly try to keep light. Accordingly, there is a need for a system or method of cooling a CVT belt within certain spatial constraints and without generating additional heat loads.